{"paper":{"title":"WKB asymptotics of meromorphic solutions of difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Alexander Fedotov (Department of Mathematical Physics), Fr\\'ed\\'eric Klopp (IMJ-PRG, SU)","submitted_at":"2019-03-06T07:55:12Z","abstract_excerpt":"We consider the difference Schr{\\''o}dinger equation $\\psi(z+h)+\\psi(z-h)+ v(z)\\psi(z)=0$ where $z$ is a complex variable and $h$ is a small positive parameter. If $v$ is an analytic function, then, for $h$ sufficiently small, the analytic solutions to this equation have standard semi-classical behavior that can be described by means of an analog of the complex WKB method for  differential equations.  In the present paper, we assume that $v$ has a simple pole and, in its neighborhood, we study the asymptotics  of meromorphic solutions to the difference Schr{\\''o}dinger equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02224","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}